Charge sharing correction methods for pixellated radiation detector arrays

ABSTRACT

Various aspects include methods of compensating for issues caused by charge sharing between pixels in pixel radiation detectors. Various aspects may include measuring radiation energy spectra with circuitry capable of registering detection events occurring simultaneous or coincident in two or more pixels, adjusting energy measurements of simultaneous-multi-pixel detection events by a charge sharing correction factor, and determining a corrected energy spectrum by adding the adjusted energy measurements of simultaneous-multi-pixel detection events to energy spectra of detection events occurring in single pixels. Adjusting energy measurements of simultaneous-multi-pixel detection events may include multiplying measured energies of simultaneous-multi-pixel detection events by a factor of one plus the charge sharing correction factor.

FIELD

The present application relates generally to radiation detectors forcomputed tomography imaging systems, and more specifically to methodsfor processing the output of pixelated radiation detectors.

BACKGROUND

In Single Photon Emission Computed Tomography (SPECT) imaging systems,gamma rays emitted from a source, such as a radiopharmaceutical orradiotracer, are detected by a detector array, such as a cadmium zinctelluride (“CZT”) detector. Other direct conversion detectors employingcadmium telluride (CdTe), gallium arsenide (GaAs), or silicon (Si), orany indirect director based on a scintillator material, may also be usedin SPECT imaging systems. Images taken at different angles are joinedtogether to reconstruct 3-dimensional images of the object underexamination.

The electrical signal generated by solid state radiation detectors, suchas CZT detectors, results from gamma-rays exciting electrons in theatoms of the material that ejects electrons from their orbits and into aconduction band of the bulk material. Each electron ejected into theconduction band leaves behind a net positive charge that behaves like apositively charged particle known as a “hole” that migrates through thematerial in response to an electric field applied between a cathode andan anode. Electrons in the conduction band are attracted by theresulting internal electric field and migrate to the anode where theyare collected creating a small current that is detected by circuitry,while the holes migrate towards the cathode.

Each gamma-ray will generate many electron-hole pairs, depending uponthe energy of the photon. For example, the ionization energy of CZT is4.64 eV, so absorbing the energy of a 140 keV gamma ray from Technetiumwill generate about 30,000 electron-hole pairs.

SUMMARY

Various aspects of the present disclosure provide methods ofcompensating for issues caused by charge sharing in pixel radiationdetectors by addressing charge-sharing phenomena. Various aspectsinclude measuring radiation energy spectra by a pixel radiation detectorcapable of registering simultaneous or coincident detection eventsoccurring in two or more pixels, adjusting energy measurements ofdetection events occurring simultaneously in two or more pixels by acharge sharing correction factor, and determining a corrected energyspectra by adding the adjusted energy measurements of detection eventsoccurring simultaneously in two or more pixels to energy spectra ofdetection events occurring in single pixels. In some aspects,determining the charge sharing correction factor may include creating afirst energy spectra for detection events occurring in single pixels anddetermining its peak value Vpeak1, creating a second energy spectra fordetection events occurring simultaneously in two or more pixels anddetermining its peak value Vpeak2, and calculating the charge sharingcorrection factor as (Vpeak1−Vpeak2)/Vpeak2. In some aspects, adjustingenergy measurements of detection events occurring simultaneously in twoor more pixels by a charge sharing correction factor may includemultiplying measured energies of detection events occurringsimultaneously into more pixels by a factor of one plus the chargesharing correction factor.

Various embodiments may be used to calibrate solid state radiationdetectors, such as CZT detectors, during design development, duringmanufacturing, and/or periodically in service.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are presented to aid in the description ofembodiments of the disclosure and are provided solely for illustrationof the embodiments and not limitation thereof.

FIG. 1 is a block diagram of a Single Photon Emission ComputedTomography (SPECT) imaging system suitable for use with variousembodiments of the present disclosure.

FIG. 2 is a conceptual cross section view diagram of a semiconductorpixel radiation detector illustrating gamma-ray interactions.

FIG. 3 is a conceptual top view diagram of a semiconductor pixelradiation detector illustrating gamma-ray interactions.

FIG. 4 a graph of cross-sections for photoelectric, Rayleigh scatteringand Compton scattering interactions in a CZT detector as a function ofphoton energy.

FIG. 5 is a diagram of gamma ray interactions in a CZT detector mayoccur according to the photoelectric effect.

FIG. 6 diagram of Compton scattering.

FIG. 7 is a graph counts vs. energy illustrating contributions ofprimary gamma rays and scattered gamma rays in a total count of gammarays measured by a radiation detector.

FIG. 8 diagram illustrating the relative path link of photo electronsversus emitted x-ray photons following photoelectric absorption of agamma photon in a CZT detector.

FIG. 9 is a diagram illustrating expansion of an electron cloud due todiffusion and repulsion affects.

FIG. 10 is a conceptual cross section view diagram of a semiconductorpixel radiation detector illustrating gamma-ray interactions that leadto charge sharing between pixels.

FIG. 11 is a conceptual top view diagram of a semiconductor pixelradiation detector illustrating gamma-ray interactions that lead tocharge sharing between pixels.

FIGS. 12A-12C are conceptual cross section view diagrams of asemiconductor pixel radiation detector illustrating migration of anelectron cloud within an inter-pixel gap.

FIG. 12D is a notional graph illustrating charge sharing betweenadjacent pixels and the effects of charge loss for photon absorptionevents occurring in the inter-pixel gap.

FIG. 13A is a top view diagram of a semiconductor pixel radiationdetector.

FIGS. 13B-13C are plots of energy spectra of detect events occurringsimultaneously between center the pixel 6 and adjacent pixels 2, 5, 7,10 shown in FIG. 13A.

FIGS. 14A and 14B are process flow diagrams illustrating methods ofcompensating for charge share affects in pixel radiation detectorsaccording to various embodiments.

FIG. 15 is a component block diagram illustrating an example serversuitable for use with the various embodiments.

DETAILED DESCRIPTION

The various embodiments will be described in detail with reference tothe accompanying drawings. Wherever possible, the same reference numberswill be used throughout the drawings to refer to the same or like parts.References made to particular examples and implementations are forillustrative purposes, and are not intended to limit the scope of theclaims. Any reference to claim elements in the singular, for example,using the articles “a,” “an,” or “the” is not to be construed aslimiting the element to the singular. The terms “example,” “exemplary,”or any term of the like are used herein to mean serving as an example,instance, or illustration. Any implementation described herein as an“example” is not necessarily to be construed as preferred oradvantageous over another implementation. The drawings are not drawn toscale. Multiple instances of an element may be duplicated where a singleinstance of the element is illustrated, unless absence of duplication ofelements is expressly described or clearly indicated otherwise.

Various embodiments of the present disclosure include methods forprocessing outputs of pixilated CZT radiation detectors used in gammaimaging systems to improve accuracy by accounting for errors due tocharge sharing between pixels.

FIG. 1 is a functional block diagram of a SPECT imaging system 100. In aSPECT imaging system 100, a subject 102 (e.g., a patient) may beinjected with a radiopharmaceutical containing a radioisotope, such astechnetium 99, that is chemically configured to be absorbed by an organor tumor to be examined creating a concentrated radiation source 104.The radiopharmaceutical within the source organ 104 emits gamma rays 106that are detected by a digital radiation detector 108 within a gammacamera 110. Count and energy data from individual pixels within thedigital radiation detector 108 are provided to an analyzer unit 112 thatanalyzes the detector data to determine the count and energy spectrum ofdetected gamma rays and provides the analyzed data to a digital imagingsystem computer 114. The analyzer unit 112 may apply calibrationcorrections including, for example, corrections for charges sharedbetween pixels is determined according to various embodiments.

The SPECT imaging system 100 may also include additional structures,such as a collimator 120 within the gamma camera 110 and a roboticmechanism (not shown) that is configured to position the gamma camera110 over the subject 102 at a variety of orientations (as illustrated in130 and 140). Positioning the gamma camera 110 at various orientationswith respect to the subject 102 enables gamma ray count and energy datato be acquired by the multi-pixel detector 108 from several differentangles. Data collected in this manner can then be processed by thedigital image system computer 114 to construct a 3D image of the organor tumor 104 where the radiopharmaceutical has accumulated.

Various alternatives to the design of the SPECT imaging system 100 ofFIG. 1 may be employed to practice embodiments of the presentdisclosure. For example, in industrial applications, such as luggagescreening, the gamma source 104 may be positioned on a far side of theobject being scanned with respect to the gamma camera and the gammaphotons imaged by the detector 106 may be photons that have passedthrough the object instead of being emitted from the object. In suchapplications, the gamma source 104 and gamma camera 110 may be bothrotated about the object, such as on a rotating frame or gantry.Further, various other types of systems that include a gamma camera thatuses a solid-state pixilated radiation detector may benefit from variousembodiments, particularly for calibrating the radiation detector duringmanufacture or in service.

The detector 106 of a SPECT imaging system may include an array ofradiation detector elements, referred to as pixel sensors. The signalsfrom the pixel sensors may be processed by a pixel detector circuit,such as an analyzer unit 112, which may sort detected photons intoenergy bins based on the energy of each photon or the voltage generatedby the received photon. When a gamma photon is detected, its energy isdetermined and the photon count for its associated energy bin isincremented. For example, if the detected energy of a photon is 64kilo-electron-volts (keV), the photon count for the energy bin of 60-80keV may be incremented. The number of energy bins may range from one toseveral, such as two to six. The greater the total number of energybins, the better the energy spectrum discrimination. Thus, the detector106 of a gamma camera 110 provides information regarding both thelocation (within pixels) of gamma photon detections and the energy ofthe detected gamma photons.

FIG. 2 illustrates a cross-sectional view of two pixels 202 a, 202 bwithin a CZT radiation detector array 200. Such a detector 200 mayinclude a sheet of CZT semiconductor crystal 208 on which are applied toa cathode 204 and the anodes 206 a, 206 b that define each pixel 202 a,202 b. The anodes 206 a, 206 b may be spaced apart by an inter-pixel gap210. In typical radiation detector arrays 200, the thickness of the CZTsemiconductor crystal 208 may range from 1 mm to 20 mm, the anodes 206a, 206 b may have a side dimension of 0.1 mm to 3 mm, and theinter-pixel gap 210 may range from 0.01 mm to 0.5 mm.

When a gamma-ray 220 is absorbed 222 by an atom within the CZTsemiconductor crystal 208, a cloud of electrons 224 a are ejected intothe conduction band of the semiconductor. Each ejected electron 224creates a corresponding hole 225 of positive charge. A voltage isapplied between the cathode 204 and anodes 206 a, 206 b causes theelectrons 224 to drift to the anode 206 a where they are collected as asignal as described above. As described more fully below, diffusion andcharge repulsion forces cause the electron cloud to expand (as shown at226) by the time the electrons reached the anode 206 a. Holes 225similarly migrate towards the cathode 204.

FIG. 3 is a top view of a portion of a pixelated radiation detectorarray 200 showing the plurality of pixels 202 a-202 aa formed by theanodes 206 a, 206 b positioned on the CZT semiconductor crystal 208. Asdescribed above, when a gamma-ray 220 interacts with atoms within theCZT semiconductor crystal 208, the ejected electrons 224 are gathered onthe nearby anode 206 c, 206 f and recorded as a count. Further, thenumber of electrons 224 (i.e., charge) collected on the anode 206 c, 206f is reflective of the energy of the incoming photon, and thus ameasurement of the energy (or spectrum) of the detected photon can bedetermined from the charge or current detected on the anodes.

A fundamental problem with accurate energy resolution when usingpixilated CZT radiation detectors is charge sharing between pixels.Charge sharing strongly depends on CZT inter-pixel gap properties, inparticular on pixel to pixel spacing 210 and the nature of the surfacepassivation. Unless the surface passivation is ideal (which it neveris), or the inter-pixel gap 210 very small (which cannot be accomplishedusing current manufacturing methods) there will be some charge-lost inthe inter-pixel gap. Further, the amount of charge loss for photonsinteracting within the inter-pixel gap 210 depends upon the passivationprocess, which can vary from fabrication lot to fabrication lot, fromdetector to detector within a fabrication lot, and even from pixel gapto pixel gap. Consequently, a correction factor to account forinter-pixel gap charge loss may need to be determined (e.g., by acalibration test) for each detector at the time of manufacture (e.g.,prior to shipment to the OEM customer). Such correction factors may alsobe determined for each inter-pixel gap to account for variations insurface passivation across each detector. Further, the inter-pixel gapcharge loss may be temperature dependent, so such calibration testingmay be performed over a range of operating temperatures for thedetector. When performed during or after fabrication, the correctionfactor(s) determined during calibration testing may be stored in FLASHmemory of the detector module so that the factor(s) can be retrieved andapplied by the OEM manufacturer of the gamma camera and/or SPECT imagingsystem.

In a typical pixilated CZT detector, charge sharing can result in 10-15%count loss for pixels with a 500 um pixel pitch. Adding an inter-pixelsteering grid (not shown) to reduce charge-sharing events would increasethe input current leakage, and so does not work well in practice.Correcting for charge-sharing in signal processing typically requireseither rejecting charge-sharing events or adding charge-sharing eventsby monitoring signals from the adjacent pixels. Rejection of thecharge-shared events leads to loss of the detector efficiency, and so istypically not acceptable as reduced efficiency requires longer scantimes and/or higher radiation doses. Adding neighboring charges does notwork either due to charge-loss in the interpixel gap.

Charge sharing is typically an undesired phenomenon in imagingapplications as the original charge induced in the CZT material is splitbetween two or more pixels. As a result, the measured energy of theincoming photon is possibly registered with a wrong energy informationand a wrong pixel location. However, when properly understood andanalyzed, charge-sharing can actually lead to an improved spatialresolution and detector efficiency as provided for in variousembodiments.

Gamma-ray photons can interact with the CZT material in various ways.The photons may be completely removed from the incident photon beam byabsorption, may be scattered after the interaction, or may pass throughthe CZT detector without any deterioration of their energy. At lowenergies of interests, such as below 200 keV, and typical sensorthickness of 5 mm, most of the incoming radiation photons are eitherabsorbed or scattered, the relative portion of each effect being highlydependent on the incoming photon energy.

The following three absorption and scattering effects are the mostrelevant: the photo-electric effect; Rayleigh scattering; and Comptonscattering. The effective photon cross section in CZT of each effect isplotted in the graph 400 that is FIG. 4. Photo-electric effect (402) isdominant in the considered energy range of 20 to 200 keV, which istypical for medical imaging. Rayleigh scattering 404 is a dominant formof scattering at lower energies. At higher energies Compton scattering406 becomes more probable. For example, a gamma-ray photon with anenergy of 122 keV will interact with a CZT radiation detector via thephoto-electric effect with an 82% probability, via the Rayleighscattering with a 7% probability, and via the Compton scattering with a11% probability.

Due to the energy dependency of the cross sections for these three typesof interactions, charge-sharing correction methods of variousembodiments work the best at energies below 200 keV, working less wellat higher energies due to Compton scattering.

The diagram 500 in FIG. 5 illustrates the photo-electric effect in whichthe energy of the interacting photon 502 is absorbed 504 by an electronthat is ejected (referred to as a “photo-electron”) from its atom andthe photon effectively disappears after the interaction. A completeabsorption of the photon energy is the desired effect for CZT imaging.The name “photo-electron” comes from a process of ejecting an electronfrom one of the atomic shells of CZT. After the ejection of thephoto-electron the atom is ionized. The vacancy in the bound shell isrefilled with an electron from the surrounding medium or from an upperatom shell. This may lead either to the emission of one or morecharacteristic fluorescence X-rays 506 or to the ejection of an electronfrom one of the outer shells called an Auger electron.

Depending whether tellurium, cadmium or zinc atoms are involved theresulting fluorescence X-ray 506 energies might be in an 8 to 31 keVrange (Te 27-31 keV; Cd 23-26 keV; Zn 8-10 keV). Therefore, in practicalterms soft X-rays events may be detected if the detection threshold isat least 31 keV, which is typically the case. This is in particularlytrue in single-photon emission spectroscopy (SPECT) that uses standardisotopes like Technetium (^(99m)Tc) that emits a 140 keV photon. Inaddition, the projected distance 510 that the fluorescence X-rays 506may travel in CZT is about 0.1 mm, which is much smaller than thetypical pixel size of 2 mm. Therefore, while fluorescence generated softX-rays 506 might show up in the tail of the measured CZT spectrum, suchsignals will likely not contribute significantly to charge sharingbetween pixels. However, it is worth noting that the generation ofsoft-X rays 506 affects the measured spectrum indirectly because thesystem will measure the energy of the absorbed photon as being less thanthe actual γ-photon energy by the amount of energy in the soft X-rays,thereby distorting the measured spectrum of radiation.

Rayleigh scattering involves photon scattering by atoms as a whole,frequently also called coherent scattering as the electrons of the atomcontribute to the interaction in a coherent manner so that there is noenergy transferred to the CZT material. The elastic scattering processchanges only the direction of the incoming photon. Rayleigh scatteringis a rather negligible effect in CZT SPECT imaging as it will not affectthe measured energy spectrum, although it may lower the cameraefficiency a bit.

Unlike Rayleigh scattering, Compton scattering involves photons that arescattered by free electrons and as a result lose some of their primaryenergy. The scattering diagram 600 in FIG. 6 illustrates that Comptonscattering 600 occurs when an incoming photon 602 imparts some of itsenergy to a free electron 604 as kinetic energy, sending the electronalong a path 608, with the resulting lower energy photon 606 scatteringthrough an angle θ. This mechanism can contribute significantly to themeasured CZT spectrum. The decrease in the photon energy that occurs ina Compton scattering event increases with increasing scattering angle θ.The energy and momentum lost by the photon 606 is transferred to oneelectron 604, called the recoil electron, which is emitted under acertain angle with respect to the direction of the incoming photon andcan have a maximum kinetic energy defining as the so-called Comptonedge. The Compton edge it is frequently visible in the spectrum measuredby a CZT radiation detector as an abrupt end to the energy tail causedby Compton scattering.

The Compton scattering equation describes the change in photon energyand its corresponding wavelength as:

${\lambda^{\prime} - \lambda} = {\frac{h}{m_{e}c}( {1 - {\cos \; \theta}} )}$

where λ is the wavelength of the photon before scattering, λ′ is thewavelength of the photon after scattering, m_(e) is the mass of theelectron, θ is the angle by which the photon's trajectory changes, h isPlanck's constant, and c is speed of light. Substituting textbook valuesfor m_(e), c and h, the characteristic Compton wavelength, defined ash/(m_(e)c), is found to be equal to 2.4 picometers (pm).

The Compton equation has two interesting properties. First, thecharacteristic Compton wavelength value is small compared to typicalgamma ray wavelengths used in medical imaging (the wavelength of a 100keV gamma ray is about 12 pm). As the result, the maximum wavelengthchange due to Compton scattering is only a fraction of the originalwavelength. Secondly, the largest change in the photon energy can onlybe expected for scattering angles θ close to 180 degrees. Thus, themaximum wavelength change is twice the Compton wavelength change.

Compton scattering also occurs within the imaging subject in SPECT aswell as in surrounding structures and the camera itself, raising theproblem of distinguishing gamma photons that are coming from the subjectof the imaging from gamma photons scattered off of other structures.Small angle Compton scattering diverts gamma photons through a smallangle that may be acceptable for imaging, but reduces the gamma photonenergy by only a small amount. In contrast, large angle Comptonscattering, which would interfere with imaging, reduces the gamma photonenergy by a significant amount. FIG. 7 illustrates in the graph 700 howthe total number of gamma photons counted by the radiation detector(line 706) will be the combination of photons traveling directly fromthe radiation source to the detector (line 702 referred to as “primary”counts) and photons that have been scattered (line 704) and thus reachedthe detector from directions away from the radiation source. FIG. 7 alsoillustrates that the difference in spectrum of scattered photonscompared to primary photons can be used to distinguish primary photonsfor imaging purposes by counting only those photons that have energieswithin an energy window 708 about the peak energy of the source gammarays. FIG. 7 ignores the effect of charge sharing between pixels, whichas described below, may result in a primary photon being measured by twoor more pixels each at an energy that is less than the energy window dueto energy being shared between the pixels.

Another factor affecting charge sharing between pixels is the size ofthe electron cloud generated when a photon is absorbed in the CZTdetector. The term “cloud” is used to highlight the fact that thephysical size of the electron charge is not a point but approximately asphere with a certain radius. Each γ-ray photon absorbed in the CZTdetector generates several thousands of electrons, so even the initialcharge has finite physical dimensions. The number of generated electronscan be estimated by dividing the incoming photon energy by the CZTionization energy of 4.64 eV. For example, a Technetium 99 gamma rayphoton with an energy of 140 keV will produce about 30,000 electrons inthe conduction zone, collectively carrying a charge of approximately 4.8femto coulombs (fC).

Compton scattering of an incoming photon 802 may result in scatteredphotons interacting with CZT at several pixel sites. At each site ofinteraction, a Compton recoil electron or photoelectron will lose energyby generating a cloud of electrons by exciting electrons into theconduction band, creating electron-hole pairs.

Similarly, the photo-electric effect may result in interactions atseveral sites as illustrated in the diagram 800 in FIG. 8. When anincoming photon 802 is absorbed by an atom in the photo-electric effect,the ejected photoelectron carries with it the energy of the photon minusthe binding energy of the particular electron ejected from the atom. Theenergy of the photoelectron is then dissipated as it excites electronsinto the conduction band (and thus generates holes), creating a cloud ofelectrons 804 along its path of travel. The range of a photoelectron inCZT depends on the energy carried off by that electron. For example, a40 keV photoelectron is stopped in CZT within about 10 μm, whereas a 100keV photoelectron is stopped in CZT within about 47 μm. The clouds ofelectrons (and holes) generated by a photoelectron are not uniform incharge density, because electron-hole production increases towards theend of the track of the photoelectron. For a 100 keV photoelectron, 30%of the electron-hole pairs are created in the last 7 μm of its trackthrough the CZT material. Additionally, an X-ray 806 of 25 keV may beproduced in the initial interaction, and such an X-ray may have meanfree path 810 of about 85 μm before it too is absorbed via thephoto-electric effect. The electron cloud 808 generated by absorption ofthe X-ray 806 will add to the overall distribution of charge in thedetector.

The proportions of interactions of gamma photons with the CZT detectorvia the photo-electric effect versus Compton scattering can becalculated using values from FIG. 4.

As the above discussion indicates, the process of electron cloudgeneration is rather complex and accurate predictions of the electroncloud size are difficult without resorting to comprehensive numericalmethods. Monte-Carlo simulations indicate that although the size of thecloud varies with the incoming photon energy, it is generally small,ranging from a few microns for low energies to several micrometers atthe higher energy end. For purposes of developing methods of the variousembodiments, and initial electron cloud radius of 10 82 m is presumedfor photons with medium energies of 122 to 140 keV. Accurate knowledgeof size of the initial electron cloud is not critical since the electroncloud is much larger by the time the charge drifts to the anode.

The electron cloud consists of several thousand individual electronsthat drift towards the anode side of the detector. Since thedistribution of electrons in the cloud is not uniform the electrons aresubject to a diffusion process governed by Fick's diffusion law. Inaddition, electrons experience electrostatic repulsion from one another.Diffusion and repulsion act together to expand the electron cloud untilthe electrons reach the anode.

As described with reference to FIG. 2, the generated electron-hole pairsseparate under the influence of the internal electric field created bythe voltage applied between the anode and cathode, with the generatedelectrons moving toward the anode. The generated holes drift towards thecathode, but as hole mobility in CZT is very low, the effect of chargesharing between pixels is dominated by the electron movements. Thus,methods for accounting for charge sharing can assume that the generatedholes do not move. The time required for electrons to separate fromholes is in the order of a nanosecond and therefore can be neglected aswell.

Referring to the diagram 900 in FIG. 9, as a photon-generated electroncloud 220 moves toward the anode 206, the size of the cloud will growdue to carrier diffusion and charge repulsion mechanisms. As the size ofthe electron cloud 226 grows due to these two effects, the electroncloud may start to become comparable to the pixel size, and thus inducecharges on adjacent pixels. Depending on the threshold voltage settingsof the SPECT read-out electronics, the charges within the electron cloudmay be detected by more than one channel or pixel using spectroscopicelectronics, such as a spectroscopic Application Specific Circuit(ASIC), capable of detecting events happening simultaneously in two ormore pixel detectors.

As a result of the diffusion and repulsion processes, electron cloudspreads uniformly in size as schematically illustrated in FIG. 9. In theexample shown in FIG. 9, the initial cloud is 67 μm wide with acharacteristic sigma of 10 μm. By the time the cloud 226 reaches theanode 206 it is 190 μm wide. This spreading effect is highly dependenton the electric filed intensity. These dimensions of the electron cloudare examples and the actual dimensions of each electron cloud will varydepending upon the energy of the incoming gamma photon, the manner inwhich the gamma photon interacts with the detector materials, thetemperature and pressure of the detector, and other factors.

Precise estimation of the diffusion spread can be obtained bynumerically solving Fick's equation in a 3-D space. However, analyticalapproximations provide useful insight. For an initial delta functioncharge distribution (zero effective cloud size), the diffusion equationcan be solved analytically to produce an effective sigma distance σ as:

σ²=4Dt_(drift)  (1)

where D is the diffusion coefficient of electrons in CZT and tdrift is adrift time from the initial interaction until the electron chargereaches the anode. The diffusion coefficient can be obtained usingEinstein's relationship:

D=μ _(n) kT/q  (2)

where μn is electron mobility in CZT.

The drift time can be obtained assuming uniform electric fielddistribution in the CZT detector, the assumption that is typically validwithin 95% of the detector body, as:

t _(drift) =d ²/(μ_(n) V)  (3)

where d is the detector thickness and V applied high voltage.Substituting (3) into (1) the following final expression is obtained:

σ²=4kTL ² /qV  (4)

The final result in equation 4 reveals that the electron cloud spreadingprocess is independent of the electron mobility value. This can beunderstood from the fact that while higher mobility leads to fasterdrift and shorter drift time it also leads to a higher diffusionconstant through Einstein's relationship. The final result in equation 4also indicates that the only physical parameters affecting the chargespreading process are the detector thickness L and the applied bias Vsince kT/q is a physical constant that is only mildly varying, as theCZT temperature is typically kept constrained in a tight range duringdetector operation.

For typical spectroscopic CZT detectors with thickness L of 5 mm andhigh-voltage bias V of 1000 V, the characteristic distance σ can becalculated from equation 4 as 50 μm. Thus, the electron cloud is about150 μm assuming 3-sigma measure and that the electron distributionwithin the cloud is Gaussian. An electron cloud of 150 μm radius iscomparable to the pixel size of 1.5-2.5 mm, which is the size of pixelstypically being used in SPECT.

It should be noted that equations 1 and 4 are first order approximationsthat take into account only a diffusion process. A more elaborateformula that takes into account both diffusion and drift is:

$\begin{matrix}{{\Delta\sigma}_{x,y,z}^{2} = {2( {D + {\frac{1}{15}( \frac{3\mu \; {Ne}}{4{\pi ɛ}_{0}ɛ_{R}} )\frac{1}{\sqrt{5}\sigma_{x,y,z}}}} )\Delta \; t}} & (5)\end{matrix}$

where the first term D represents a diffusion process while the secondterm represents drift. N is the number of electrons in the charge cloud,e is the electron charge and εR is CZT relative permittivity. Note thatequation 5 simplifies to equation 1 if the drift process is neglected.An interesting observation provided by equation 5 is that the driftrepulsion effect increases with the number of electrons N, and thus,charge-sharing effects increase with the photon energy.

FIG. 10 is a cross-section diagram of two pixels 202 a, 202 b within aCZT detector 200 illustrating the various interactions and sources ofcross sharing of charge clouds discussed above. As described withreference to FIG. 2, nominally gamma rays 220 will interact by thephotoelectric effect and/or Compton scattering at one or more events222, resulting in an electron cloud 224 a that drift towards the anode206 a and a corresponding cloud of holes 225 that drift toward thecathode 204. As noted above, the electron cloud will expand in diameterdue to diffusion and repulsion is shown at 226 a, but if the interaction222 occurs away from the boundaries of the pixel 202 a, the entirecharge of the electron cloud will be collected on the anode 206 a.

If the incoming gamma-ray 220 interacts with the CZT detector materialvia Compton scattering 1012 close to a boundary of a pixel 202 a, arecoil electron may produce a local electron cloud 1014 in that pixel202 a, while the recoil gamma-ray follows a path 1010 that terminates inan adjacent pixel 202 b via a photoelectric effect event 1016 thatejects a photoelectron that produces an electron cloud 1018. In thissituation, the charge resulting from the electron cloud 1014 generatedby the Compton scattering event 1012 will be collected by the firstpixel's anode 206 a, while the charge resulting from the electron cloud1018 generated by the photoelectric affect event 1016 will be collectedby the second pixel's anode 206 b. When this happens, counsel berecorded in both pixels 202 a, 202 b but with lower energies then thatof the incoming gamma ray 220.

If the incoming gamma-ray 220 interacts with the CZT detector materialvia the photo electric effect close to a boundary of a pixel 202 a asillustrated in event 1022, the resulting electron cloud 1024 may expandunder diffusion and repulsion processes to encompass both the anode 206a of that pixel (portion 1026 a) and the anode 206 b of the adjacentpixel 202 b (portion 1026 b). Additionally, some of the charge in theexpanded electron cloud may be trapped in surface defects within the CZTmaterial 208 between the two pixels (portion 1026 c). Such chargesharing will result in signals recorded on two pixel anodes 206 a, 206 bfor the single absorption event 1022, but at energies lower than that ofthe incoming photon 220.

Some incoming gamma-rays 220 will also interact with the CZT detectormaterial between two pixels 202 a, 202 b as illustrated in event 1030,because the pixels are positioned a finite distance apart. In somecases, the resulting electron cloud 1032 may expand under diffusion andrepulsion processes sufficient to encompass both anodes 206 a, 206 b,with some of the charge in the expanded electron cloud being trapped insurface defects within the CZT material 208 between the two pixels. Insuch cases, the charge sharing will result in signals recorded on two(or more) pixel anodes 206 a, 206 b for the single absorption event1022, but at energies lower than that of the incoming photon 220. Inother cases, such as when the inter-pixel photon interaction 1030 occursnear the anodes 206 a, 206 b, there may be insufficient time for theresulting electron cloud 1032 to expand sufficiently to encompass one orboth of the adjacent anodes 206 a, 206 b, in which case the charge maybe trapped in surface defects of the inter-pixel material 208 with nocount.

FIG. 11 illustrates the charge sharing events from a top view of apixelated CZT radiation detector 200. In addition to the absorption ofevents with electron clouds 224 retained within the pixels describedwith reference to FIG. 2, some gamma rays will interact with thedetector 200 between pixels or close to the boundary of axles resultingin charge sharing between two or more pixels. For example, a photonabsorbed between two pixels as illustrated in event 1102 may result inthe electron cloud 1102 being shared between the two adjacent pixels 202a, 202 b. As another example, a gamma-ray photon 220 may generate afirst electron cloud 1104 in a first pixel 202 d via a Comptonscattering event and generate a second electron cloud 1106 when therecoil photon is absorbed a second pixel 202 i such as via thephotoelectric effect. As a further example, a gamma-ray photon 220 maybe absorbed within the inter-pixel volume between three or four pixels202 i, 202 j, 202 m, 202 n, in which case some of the resulting electroncloud 1108 may be absorbed in any one or all of the adjacent pixels, aswell as within surface defects within the inter-pixel space.

Charge sharing effects that may occur when photon interactions occurwithin the inter-pixel volume is further illustrated in FIGS. 12A-12C.

Referring to FIG. 12A, a charge cloud 1224 generated due to a gamma-rayinteraction within an inter-pixel gap but close to the CZT cathode closeto the boundary of a pixel 202 a, the charge 1226 may drift towards onlyone pixel 202 a under the influence of the applied electric field thatpixel's anode 206 a.

Referring to FIG. 12B, a charge cloud 1224 generated due to a gamma-rayinteraction close to the CZT cathode and towards the middle of aninter-pixel gap, the charge 1226 may split under the influence of themagnetic field generated by the anodes 206 a, 206 b of adjoining pixels202 a, 202 b, resulting in two charges 1226 a, 1226 b that may bedetected by the respective pixels. As the charge 126 is split into twocharges 1226 a, 1226 b, the signals measured by the pixels 202 a, 202 bwill be less than present in the initial charge cloud 1224 and may notbe equal.

The movement of charges illustrated in FIGS. 12A and 12B somewhatsimplistic because the illustrations neglect surface effects at theinter-pixel gap. Experimental data has confirmed that imperfections inthe surface passivation of the CZT material in the inter-pixel gapsurface can result in absorption of some of the charge cloud that fallswithin the gap. This is illustrated in FIG. 12C, which shows that aportion 1226 c of the charge drifting in the inter-pixel gap is trappedby a surface region. Modeling of the portion of the charge trapped bythe surface region in the inter-pixel gap is difficult as the electricfield there has both vertical and lateral components. In addition, thesurface region may contain significant number of trapping sites (surfaceshallow and deep level traps) due to imperfect passivation of the CZTmaterial. However, some simplifying assumptions may enable estimatingthe effects of this charge-loss phenomena. At the surface, electronsexperience a small electric field in the lateral (anode to anode)direction compared to the vertical (cathode to anode) direction fieldthat drove movement from the place of the photon interaction. However,the electron cloud is still subject to the diffusion process, and aslong as the electron cloud remains at or near the surface of theinter-pixel gap the charge will diffuse towards the adjacent pixels evenif the cloud is much closer to one of the pixels than the other. Theexact portion of the charge going to the adjoining pixels may beestimated based on the physical position of the cloud with respect tothe two pixels 202 a, 202 b.

FIG. 12D illustrates graphically how the amount of charge loss due tocharges being trapped by the surface region in the inter-pixel gap mayaffect the amount of charge gathered and thus detected photon energy(keV) measured by adjacent pixels. The graph 1240 illustrates how whenthere is no charge loss due to surface effects or deep traps (line1244), the sum of the energies measured in the adjoining pixels willequal the actual energy E0 of the detected photon (i.e., E0=E1+E2). Whenthe inter-pixel gap exhibits some charge loss (lines 1246 and 1248), thesum of the energies measured in the adjoining pixels (i.e., E1+E2) willbe less than the energy of the detected photon due to the charge loss(CL), and thus E0=E1+E2+CL. Further, the effect of inter-pixel chargeloss is greatest when photons are stopped in the middle between twopixels (i.e., close to where E1=E2), and decreases toward zero as themeasured energy is increasingly measured in just one pixel. Fordetectors that exhibit a small inter-pixel gap charge loss asillustrated in line 1246, the charge loss CL may be small enough thatthe photon energy E0 is approximately equal to the sum of the energiesmeasured by two pixels (i.e., E0≈E1+E2). However, for detectors thatexhibit a large inter-pixel gap charge loss as illustrated in line 1246,as may be the case for detectors with a relatively large inter-pixelspace and/or poor surface passivation, the charge loss CL may besignificant, leading to errors in measured spectrum.

Experiments using Cd_(0.9)Zn_(0.1)Te detectors with various thickness(from 2 mm to 5 mm) made using various ways of manufacturing thepassivation and measured with either spectroscopic or photon countingelectronics, measured inter-pixel charge loss to be 10-15%, althoughoccasionally much larger losses were observed for large (relative to thepixel size) inter-pixels gaps. The inter-pixel charge losses weredominated by double-pixel events as triple and multiple events (morethan 3 pixels triggered at the same time such as 1108 in FIG. 11) wereobserved to be insignificant with low numbers of detected events.

In experiments, charge sharing results were obtained using a ⁵⁷Co sourceilluminating two different 4×4 pixel array detectors having theconfiguration illustrated in FIG. 13A. One array detector had a gapbetween the pixel electrodes of 0.1 mm, and the other array detector hada gap of 0.46 mm, both with a 2.46 mm pixel pitch. In these experiments,the pixel count data were recorded with a bias voltage of −300V and−800V at a temperature of 22° C. The average total electronic noise forthe setup was 2.5 keV FWHM. The energy resolution of the detectorsamples (for the single pixel events) for all pixels was measured tovary between 5 and 9 keV FWHM at the 122 keV peak. Charge sharing eventsbetween pixels were observed by detecting coincident events in adjacentpixels. The time coincident spectra were recorded with a bias voltage of−800V at a temperature of 22° C. Plots of shared events between centerpixel 6 and adjacent pixels 2, 5, 7 and 10 in FIG. 13A that wereobserved in experiments are presented in FIG. 13B for the array detectorwith a gap between the pixel electrodes of 0.46 mm, and in FIG. 13C forthe array detector with a gap between the pixel electrodes of 0.1 mm.

Comparing FIGS. 13B and 13C, a clear pulse height loss for charge sharedevents appears most pronounced for the detector with the larger pixelgap (FIG. 13B). This effect is illustrated in FIGS. 13B and 13C using a2D representation that gives the pulse height of shared events betweenone pixel (i.e., pixel 6 in FIG. 13A) and its neighbors (i.e., pixels 2,5, 7 and 10 in FIG. 13A).

Ideally, the sum of the energies recorded as shared events by two pixelsshould add up to the full energy E0=E1+E2, as illustrated in line 1244of FIG. 12D. This would be showing in FIGS. 13B and 13C as a straightline E2=E0−E1. That is approximately the case in FIG. 13C for theinter-pixel gap of 100 um, although some slight departure from linearitycan be observed, as illustrated in line 1246 in FIG. 12D. However, the2D plots in FIG. 13B show a clear bending for the 0.46 mm gap data. Thecurvature shows that the shared events do not have 100% efficient chargecollection and that charge loss is the largest for those events that arestopped in the middle between two pixels, as illustrated in line 1248 inFIG. 12D. Moreover, this charge loss increases with the pixel gap. Theresults indicate that charge from the events stopped in between thepixels (e.g., events 1030 in FIG. 10) in detector arrays with large gapsbetween pixels will end up in the surface layer between the pixels andthat charge effectively is trapped there. These events will thereforenot induce their full signal in the pixel electrodes leading to errorsin measured spectrum.

The result of this analysis and experimental data were used to developthe embodiment methods for accounting charge sharing between pixels of apixelated radiation detector.

FIG. 14A illustrates a method 1400 for calibrating pixel radiationdetectors and adjusting the output of such detectors to account forcharge sharing effects according to various embodiments. The method 1400may be implemented by a processor of a computing device (e.g., thecomputer 112 of FIG. 1 or the computing device 1500 of FIG. 15).

In step 1402, the processor may measure the energy spectra of radiationreceived on a pixel radiation detector from an Am241 or Co57 sourceusing any suitable spectroscopic ASIC device that has capability toregister simultaneous, coincidence events on multiple pixels.

In step 1404, the processor may create a first energy spectra fordetection events occurring in single pixels and determining its peakvalue V_(peak1). In some embodiments, the processor may create the firstspectra for the non-charge-shared events detected by the spectroscopicASIC device, and use the results to determine a peak value V_(peak1)using normal analysis algorithms.

In step 1406, the processor may create a second energy spectra fordetection events occurring simultaneously in two or more pixels anddetermining its peak value V_(peak2). In some embodiments the processormay create the second spectra for all charge-shared events detected bythe spectroscopic ASIC device, and use the results to determine a peakvalue V_(peak2).

In step 1408, the processor may determine a charge sharing correctionfactor (CSCF) as a function of the photon energy in adjoining pixelsusing data obtained from calibration data, such as illustrated in FIGS.13B and 13C. As illustrated in FIG. 12D, inter-pixel charge loss will begreatest when the charges measured by the adjoining pixels is equal ornearly equal, and decreases asymptotically as the difference in measuredenergy between the two pixels increases. Thus, the photon energiesmeasured in adjacent pixels in a two-pixel charge-sharing scenario willbe divided between the two pixels minus the charge loss. For example, ifthe photon energy is 60 keV, the measured energies between the twopixels may be 24 keV and 34 keV or 25 keV and 35 keV. When the energiesmeasured in the adjacent pixels is equal, the charge loss (say 10 keV)will be greatest, so the 60 keV photon will be measured as two photonsof 25 keV in adjoining pixels with 10 keV consumed by the inter-pixelcharge loss. When the energies are not equally divided between the twopixels, the inter-pixel gap charge loss will be smaller. For example,the 60 keV photon might be measured as two photons of 20 keV and 32 keVin the adjoining pixels with 8 keV consumed by the inter-pixel chargeloss. The closer the measured energy in one pixel approaches that of theabsorbed photon, the less the energy that will be consumed by theinter-pixel charge loss. By collecting data on measured energies inadjoining pixels from inter-pixel gap events during a calibrationexposure, a charge sharing correction factor can be determined thataccounts for observed charge sharing losses.

In step 1410, the processor may adjust energy measurements of detectionevents occurring simultaneously in two or more pixels by a chargesharing correction factor. In particular the processor may multiply theenergy of all detected charge-shared events by (1+CSCF), effectivelyshifting the energy of these events to the higher energies by thecorrection factor. For example, the charge sharing correction factor mayshift energies of inter-pixel events by 10-15%.

In step 1412, the processor may determine a corrected energy spectrum byadding the adjusted energy measurements of detection events occurringsimultaneously in two or more pixels to energy spectra of detectionevents occurring in single pixels. Thus, the processor may combine thenon-charge-shared events with all charge-shared events corrected by thecharge sharing correction factor to create one spectrum with the peakadjusted to V_(peak1).

The combined spectra created in step 1412 will offer accurate spectrawith efficiency than achieved using conventional correction methods.Experiments have shown an in increase in efficiency of 40-50% whilemaintaining accurate energy resolution compared to other methods.

In various embodiments, the operations in steps 1402-1408 may beperformed during a calibration procedure, such as during manufacture ofthe radiation detector and/or during service of a gamma camera using agamma source with a known gamma ray energy and flux, while theoperations in steps 1410 and 1412 are performed during imagingoperations of the gamma camera.

FIG. 14B illustrates another method 1450 for calibrating pixel radiationdetectors and adjusting the output of such detectors to account forcharge sharing effects according to another embodiment. The method 1450may be implemented by a processor of a computing device (e.g., thecomputer 112 of FIG. 1 or the computing device 1500 of FIG. 15).

In the method 1450 the steps 1402 to 1406 may be performed as describedabove for the method 1400.

In step 1452, the processor may calculate the charge sharing correctionfactor (CSCF) using the formula (V_(peak1)−V_(peak2))/V_(peak2).Typically this will be about 10-15%, but may be larger for detectorswith a large inter-pixel gap with respect to the pixel pitch. Dependingupon the inter-pixel gap and the quality of the surface passivation,this number can vary from 0 to 50%.

In various embodiments, the operations in steps 1402-1406 and 1452 maybe performed during a calibration procedure, such as during manufactureof the radiation detector and/or during service of a gamma camera usinga gamma source with a known gamma ray energy and flux. The operations insteps 1410 and 1412 are performed as described above for the method 1400during imaging operations of the gamma camera.

The calibration operations illustrated in the embodiment methods 1400and 1450 may be performed after manufacturing on a per detector basis inorder to accommodate differences in inter-pixel gap charge lossresulting from differences in surface passivation that may occur fromfabrication lot to fabrication lot, from detector to detector within afabrication lot. Alternatively, the calibration operations illustratedin the embodiment methods 1400 and 1450 may be performed after detectorshave been assembled into a gamma camera, such as part of initial and/orperiodic calibrating the camera and imaging system. The calibrationoperations illustrated in the embodiment methods 1400 and 1450 may berepeated across a range of temperatures at which the detector isexpected to operate. Further, the calibration factors determined insteps 1408 and 1452 may be determined for each inter-pixel gap toaccount for the differences in surface passivation across each detector.

When the calibration operations in steps 1408 and 1452 are performedduring or after fabrication, the correction factor(s) determined duringcalibration testing may be stored in FLASH memory of the detector moduleas part of steps 1408 and 1452, so that the correction factors areavailable for use in steps 1410 during operation of the detector. Whenthe calibration operations in steps 1408 and 1452 are performed afterassembly of the imaging system (e.g., a SPECT system), the correctionfactor(s) determined during calibration testing may be stored in memoryof an analysis unit (e.g., 110) as part of steps 1408 and 1452, so thatthe correction factors are available for use in steps 1410 duringoperation of the imaging system.

The various embodiments (including, but not limited to, embodimentsdescribed above with reference to FIGS. 14A and 14B) may also beimplemented in computing systems, such as any of a variety ofcommercially available servers. An example server 1500 is illustrated inFIG. 15. Such a server 1500 typically includes one or more multicoreprocessor assemblies 1501 coupled to volatile memory 1502 and a largecapacity nonvolatile memory, such as a disk drive 1504. As illustratedin FIG. 15, multicore processor assemblies 1501 may be added to theserver 1500 by inserting them into the racks of the assembly. The server1500 may also include a floppy disc drive, compact disc (CD) or digitalversatile disc (DVD) disc drive 1506 coupled to the processor 1501. Theserver 1500 may also include network access ports 1503 coupled to themulticore processor assemblies 1501 for establishing network interfaceconnections with a network 1505, such as a local area network coupled toother broadcast system computers and servers, the Internet, the publicswitched telephone network, and/or a cellular data network (e.g., CDMA,TDMA, GSM, PCS, 3G, 4G, LTE, or any other type of cellular datanetwork).

Computer program code or “program code” for execution on a programmableprocessor for carrying out operations of the various embodiments may bewritten in a high level programming language such as C, C++, C#,Smalltalk, Java, JavaScript, Visual Basic, a Structured Query Language(e.g., Transact-SQL), Perl, or in various other programming languages.Program code or programs stored on a computer readable storage medium asused in this application may refer to machine language code (such asobject code) whose format is understandable by a processor.

The present embodiments may be implemented in systems used for medicalimaging, Single Photon Emission Computed Tomography (SPECT) for medicalapplications, and for non-medical imaging applications, such as inbaggage security scanning and industrial inspection applications.

Charge sharing effects in pixel radiation detectors may cause efficiencyvariations and spectral degradation. In a photon counting system, like aSPECT system, such events can be missed or double-counted, depending onthe detector settings. The effect depends on the pixel geometry,detector thickness, electric field and the size of the charge cloudspreads as it drifts towards the anodes. In spectroscopic systems, suchas SPECT, charge-sharing events are even more harmful as they disturbreadings of the gamma-ray photons. Charge sharing, if left uncorrected,may lead to lower detector efficiency, increased spectrum tail anddecreased energy resolution.

The various embodiments overcome these issues caused by charge sharingin pixel radiation detectors by providing a method that properly treatsthe charge-sharing phenomena by precise calibration of CZT pixelradiation detectors. The methods of various embodiments apply inparticular to spectroscopic applications, and for systems that usesmall-pixel detectors in SPECT. In particular, various embodimentsinclude measuring radiation energy spectra by a pixel radiation detectorcapable of registering simultaneous, coincident detection eventsoccurring in two or more pixels, adjusting energy measurements ofdetection events occurring simultaneously in two or more pixels by acharge sharing correction factor, and determining a corrected energyspectra by adding the adjusted energy measurements of detection eventsoccurring simultaneously in two or more pixels to energy spectra ofdetection events occurring in single pixels. In some embodiments,determining the charge sharing correction factor may include creating afirst energy spectra for detection events occurring in single pixels anddetermining its peak value Vpeak1, creating a second energy spectra fordetection events occurring simultaneously in two or more pixels anddetermining its peak value Vpeak2, and calculating the charge sharingcorrection factor as (Vpeak1−Vpeak2)/Vpeak2. In some embodiments,adjusting energy measurements of detection events occurringsimultaneously in two or more pixels by a charge sharing correctionfactor may include multiplying measured energies of detection eventsoccurring simultaneously into more pixels by a factor of one plus thecharge sharing correction factor.

While the disclosure has been described in terms of specificembodiments, it is evident in view of the foregoing description thatnumerous alternatives, modifications and variations will be apparent tothose skilled in the art. Each of the embodiments described herein maybe implemented individually or in combination with any other embodimentunless expressly stated otherwise or clearly incompatible. Accordingly,the disclosure is intended to encompass all such alternatives,modifications and variations which fall within the scope and spirit ofthe disclosure and the following claims.

What is claimed is:
 1. A method for correcting spectra measured by apixel radiation detector to account for inter-pixel charge sharingeffects, comprising: measuring radiation energy spectra by a pixelradiation detector capable of registering simultaneous, coincidentdetection events occurring in two or more pixels; adjusting energymeasurements of detection events occurring simultaneously in two or morepixels by a charge sharing correction factor; and determining acorrected energy spectrum by adding the adjusted energy measurements ofdetection events occurring simultaneously in two or more pixels toenergy spectra of detection events occurring in single pixels.
 2. Themethod of claim 1, further comprising determining the charge sharingcorrection factor by: creating an energy spectrum for detection eventsoccurring simultaneously in two or more pixels; and determining thecharge sharing correction factor based upon an energy of gamma photonsfrom a known source and energies measured in adjoining pixels insimultaneous detection events to account for after pixel charge losseffects.
 3. The method of claim 2, wherein adjusting energy measurementsof detection events occurring simultaneously in two or more pixels by acharge sharing correction factor comprises multiplying measured energiesof detection events occurring simultaneously into more pixels by afactor of one plus the charge sharing correction factor.
 4. The methodof claim 1, further comprising determining the charge sharing correctionfactor by: creating a first energy spectra for detection eventsoccurring in single pixels and determining its peak value V_(peak1);creating a second energy spectra for detection events occurringsimultaneously in two or more pixels and determining its peak valueV_(peak2); and calculating the charge sharing correction factor as(V_(peak1)−V_(peak2))/V_(peak2).
 5. The method of claim 4, whereinadjusting energy measurements of detection events occurringsimultaneously in two or more pixels by a charge sharing correctionfactor comprises multiplying measured energies of detection eventsoccurring simultaneously into more pixels by a factor of one plus thecharge sharing correction factor.
 6. A method of calibrating a pixelradiation detector to account for inter-pixel charge sharing effects,comprising: measuring radiation energy spectra from a radiation sourcehaving a known gamma photon energy by the pixel radiation detector usingelectronics capable of registering simultaneous, coincident detectionevents occurring in two or more pixels; recording energies measured inadjoining pixels for detection events occurring simultaneously in two ormore pixels; and determining a charge sharing correction factor basedupon the radiation source known gamma photon energy and recordedenergies measured in adjoining pixels for detection events occurringsimultaneously in two or more pixels.
 7. The method of claim 6, whereindetermining a charge sharing correction factor based upon the radiationsource known gamma photon energy and recorded energies measured inadjoining pixels for detection events occurring simultaneously in two ormore pixels accounts for inter-pixel gap charge loss as a function of adifference between energies measured in adjoining pixels.
 8. The methodof claim 6, wherein determining a charge sharing correction factor basedupon the radiation source known gamma photon energy and recordedenergies measured in adjoining pixels for detection events occurringsimultaneously in two or more pixels comprises: creating a first energyspectra for detection events occurring in single pixels and determiningits peak value V_(peak1); creating a second energy spectra for detectionevents occurring simultaneously in two or more pixels and determiningits peak value V_(peak2); and calculating the charge sharing correctionfactor as (V_(peak1)−V_(peak2))/V_(peak2).
 9. The method of claim 6,where in the method is performed as part of manufacturing the pixelradiation detector.
 10. The method of claim 9, further comprisingstoring the charge sharing correction factor in memory associated withthe pixel radiation detector.
 11. A Single Photon Emission ComputedTomography (SPECT) imaging system, comprising: a pixel radiationdetector; and an analysis unit configured to receive data from the pixelradiation detector and output analyzed data to a digital imageprocessing computer, wherein the analysis unit is configured to performoperations of: adjusting energy measurements of detection eventsoccurring simultaneously in two or more pixels by a charge sharingcorrection factor; and determining a corrected energy spectrum by addingthe adjusted energy measurements of detection events occurringsimultaneously in two or more pixels to energy spectra of detectionevents occurring in single pixels.
 12. The SPECT imaging system of claim11, wherein the analysis unit is further configured to performoperations comprising performing a calibration procedure by: recordingenergies measured in adjoining pixels of the pixel radiation detectorfor detection events occurring simultaneously in two or more pixelswhile being exposed to gamma radiation from radiation source having aknown gamma photon energy; and determining the charge sharing correctionfactor based upon the radiation source known gamma photon energy andrecorded energies measured in adjoining pixels for detection eventsoccurring simultaneously in two or more pixels.
 13. The SPECT imagingsystem of claim 12, wherein determining the charge sharing correctionfactor based upon the radiation source known gamma photon energy andrecorded energies measured in adjoining pixels for detection eventsoccurring simultaneously in two or more pixels accounts for inter-pixelgap charge loss as a function of a difference between energies measuredin adjoining pixels.
 14. The SPECT imaging system of claim 12, whereindetermining the charge sharing correction factor based upon theradiation source known gamma photon energy and recorded energiesmeasured in adjoining pixels for detection events occurringsimultaneously in two or more pixels comprises: creating a first energyspectra for detection events occurring in single pixels and determiningits peak value V_(peak1); creating a second energy spectra for detectionevents occurring simultaneously in two or more pixels and determiningits peak value V_(peak2); and calculating the charge sharing correctionfactor as (V_(peak1)−V_(peak2)) V_(peak2).